The central instrument for the present study is a modified version of the 35 GHz cloud radar MIRA-35, which is operated in SLDR mode. MIRA-35 in general is a dual-polarization (LDR-mode) radar which emits linearly polarized radiation through the co-channel, while the returned signals are received in both the co- and cross-channels. The SLDR mode cloud radar was implemented based on the conventional linear depolarization ratio (LDR) mode by 45∘ rotation of the antenna system around the emission direction. While numerous polarimetric configurations of radar systems exist Chap. 6, the LDR mode is currently the most common one among cloud radars. The properties of the standard LDR mode MIRA-35 are elaborated in detail in . The technical characteristics of MIRA-35 used in the CyCARE campaign in Limassol, Cyprus, are given in Table .

Standard vertical-stare LDR-mode allows us only to discriminate between hydrometeors with an isometric intersection and with a columnar intersection , i.e., aggregates cannot be separated from generally horizontally oriented plate-like particles in vertical-stare mode because their scattering intersections appear to be similar. In order to optimize the MIRA-35 cloud radar for improved measurements of hydrometeor shape and orientation, two modifications were applied to the standard setup as it is described by . First, the cloud radar was mounted onto a positioner platform which allows for a freely definable position of the radar within a half sphere given by 360∘ of azimuth and 180∘ of elevation. The second modification addresses a 45∘ rotation of the antenna around the emission direction. This operation mode, in general defined as SLDR mode, has specific advantages in studies of the intrinsic relationship between the polarimetric signature of the particle shape and radar elevation angle. In contrast to the standard LDR mode, variations in the orientation of hydrometeors only have small effects on the measured SLDR, even at low elevation angles . In turn, SLDR in vertical pointing mode (elevation =90∘) is similar to the LDR observed with standard MIRA-35 systems. This behavior is also of advantage because it ensures direct comparability with other standard LDR-mode radars in vertical-pointing measurements. In the framework of the present study, the radar was steered toward geographic south direction (180∘ azimuth angle) and performed range-height indicator (RHI) scans from 90∘ (zenith-pointing) to 150∘, corresponding to 30∘ elevation over the horizon toward north direction. This notation of the elevation angle range will be used throughout this article and figures.

Figure  describes the setup of one scan cycle as it was applied in the measurements of the SLDR mode MIRA-35, used in this study. Each scan cycle starts at minute 29 of each hour. Within 6.5 min, two RHI scans from 90 to 150∘ and from 150 to 90∘ elevation angle and one plan-position indicator (PPI) scan at 75∘ elevation are performed. During the remaining 53.5 min of each measurement hour, vertical-stare observations (at 90∘ elevation angle) are performed to support standard retrievals, such as done within Cloudnet or as required for Doppler-spectra analysis techniques . A limit of 150∘ elevation angle was established to avoid physical barriers such as trees or buildings. It is also a reasonable compromise between the required horizontal homogeneity and the intensity of the SLDR gradient produced by the observed hydrometeors. As the detailed procedure of data acquisition was depicted by and , the determination of the polarimetric parameters required for this study is only briefly outlined below. The primary measurement parameters are thus the Doppler power spectra received by the detectors in the co- and cross-channels with respect to the emitted polarization plane Pco(ωk) and Pcx(ωk), respectively, with ωk being the Doppler frequency shift of each individual spectral component k. The herein presented VDPS method only considers the main peak of the detected Doppler spectrum in the co-channel. Thus, in a next step, each data point is screened for the spectral component ωkmax where Pco(ωk) is maximal. The following parameter is then only calculated for the Doppler spectral bin ωkmax. The frequency dependency is thus omitted in the following and the polarimetric properties linear depolarization ratio in slanted mode (SLDR) can be derived as follows: 1SLDR=〈Pcx〉〈Pco〉, where 〈〉 denotes averaging over a number of collected Doppler spectra.

The raw spectra of the signal-to-noise ratio (SNR) are subject to noise artifacts. Correspondingly, a noise filtering is performed to remove values which are below a given threshold value 2n=m+3σ, with m being the mean and σ being the standard deviation of noise in the co-channel. The properties of the noise in the co-channel are estimated from the last five range gates of each profile assuming no scattering is present. A spectral line with the power in the cross channel below n is excluded from the following analysis.

An important technical aspect which needs to be considered in the data analysis is the leakage of a fraction of signal from the co-channel into the cross-channel. The co-cross-channel isolation was determined with the experimental approach described by , by means of identification of the minimum SLDR value that was measured at zenith-pointing, in the presence of light drizzle. The co-cross-channel isolation used in this study was thus found to be -35 dB with MIRA-35.

MIRA-35 is operated as part of the Leipzig Aerosol and Cloud Remote Observations System (LACROS, ), a suite of ground-based instruments of the Leibniz Institute for Tropospheric Research (TROPOS). Besides the SLDR-mode Ka-band scanning cloud radar, LACROS comprises an extensive set of active and passive remote sensing instruments for the characterization of aerosol properties, clouds, and precipitation, including multi-wavelength polarization lidar, Doppler lidar, microwave radiometer, and optical disdrometer. Data used in this study were acquired in the framework of a deployment of LACROS at the Mediterranean site of Limassol, Cyprus (34.68∘ N, 33.04∘ E, 10 m a.s.l.) during the CyCARE field campaign . The region of Cyprus is a relevant location for studies of the impact of aerosol on cloud processes because of a large variety of air pollutants, desert dust, and marine salt particles in the atmosphere above the island. The CyCARE campaign was conducted from September 2016 to March 2018 and aimed at the determination of the relationship between aerosol properties and the formation of cirrus and mixed-phase clouds in the heterogeneous freezing regime.

The VDPS method combines simulations of SLDR^ (thereby and hereafter, the symbol ^ denotes simulated parameters) with measurements of SLDR (see Sect. ). The study is based on the same set of equations as was previously presented by . The theoretical framework assumes Rayleigh scattering and utilizes a spheroidal approximation of particle shape . In the scattering model used, polarimetric variables depend on two parameters: the polarizability ratio ξ, which describes the particles by means of a density-weighted axis ratio, and the degree of orientation κ, which is a measure of the preferred orientation of the spheroids population. It is well known that the Rayleigh approximation is not always applicable to simulate scattering from individual and large ice particles at wavelengths shorter than C-band, which holds especially for absolute values such as reflectivity factor . At shorter wavelengths, the direct dipole approximation (DDA, ) can be used to simulate scattering of individual ice particles having a complex shape. Meanwhile, extensive databases exist and have found, e.g., special attention already for the application of multi-wavelength radar studies . However, these simulations and associated studies are often limited to a number of predefined shapes and therefore do not necessarily represent the realistic distribution of ice particles observed by a radar . Simulations for a single particle also do not reflect the volumetric scattering effects of a large population of hydrometeors. In general, ice particles in a scattering volume have arbitrary shapes and the contribution of individual particles to the backscattering radar observables and especially polarimetric quantities is averaged out . We decided to assume the Rayleigh scattering and the spheroidal particle approximation because (1) such a model explains general polarimetric scattering effects with just a few parameters (axis ratio, permittivity, and canting angle), (2) the model parameters are well constrained by the observations, (3) the volumetric scattering is taken into account, and (4) the model enables a computationally effective derivation of the polarizability ratio. In this study, we sort particles into three primary categories based on their shape: oblate particles, which have a polarizability ratio less than 1, prolate particles, characterized by a polarizability ratio greater than 1, and isometric particles, where the polarizability ratio ranges from 0.8 to 1.2, depending on the radar calibration (see Table ). With respect to the definition in this study, we consider particles as isometric when they do not produce considerable polarimetric signatures. Such particles have either spherical or just slightly non-spherical shape. In the case of particles with a low refractive index (i.e., low permittivity), their reduced response to radar waves may lead to scattering characteristics that resemble those of isometric particles.

Figure  shows the dependencies of SLDR^ on the polarizability ratio and degree of orientation of ice particles at 90∘ (zenith) and 150∘ (60∘ off-zenith) elevation angle. Figures a and b show that SLDR^ is mostly sensitive to ξ (as noted by ), which demonstrates the relevance of using SLDR rather than Differential Reflectivity (ZDR) to determine the particle shape. For our radar configuration, the realistic range of possible polarizability ratios ξ spans from 0.3 to 2.3 and the degree of orientation κ ranges from -1 to 1. κ will only be briefly elaborated in this section as it will be used only qualitatively in the frame of this study. In the case of spheroidal approximation and Rayleigh scattering regime, the polarizability ratio ξ, describing the shape of particles, is a function of permittivity and axis ratio and is independent of the particle volume. A polarizability ratio ξ=1 designates spherical particles or particles with low density, while ξ<1 and ξ>1 describe oblate and prolate particles, respectively. Also for non-isometric particles, a decrease in apparent particle density causes ξ to approach a value of unity . The degree of orientation characterizes the width of the particle orientation angle distribution (the degree of orientation is explained in more detail in , in their Fig. 9 and Eq. (11)). For instance, |κ|=0 corresponds to uniform distribution, while |κ|=1 indicates that all particles are aligned in the same way. The sign of κ indicates the preferable orientation of the symmetry axis, i.e., κ=+1 indicates that all particles are aligned and have a vertical symmetry axis, κ=-1 corresponds to the case when particles have a predominantly horizontally aligned symmetry axis. We therefore assume κ>=0 for oblate particles and κ<=0 for prolate particles. Regarding Fig. a and b we consider that κ≈-0.3 corresponds to randomly oriented isometric particles when SLDR is minimal and these values do not depend on the elevation angle .

A subset from Fig.  is presented in Fig. 3 in order to demonstrate the general, idealized relationship between SLDR^ and elevation angle for the main particle shape classes oblate (“+”), isometric (“o”), and prolate (“-”), thereby assuming predominantly horizontal orientation. Indeed, the “+” symbol is located in the oblate domain (zone A) described by a polarizability ratio ξ=0.35 and a degree of orientation κ=0.85 representing horizontally oriented plate-like particles, while the “*” symbol is located in the prolate domain (zone B) described by ξ=2.15 and κ=-0.85 representing horizontally oriented columnar crystals. The symbol ”o” is determined by ξ=1 and κ=-0.4, such as randomly oriented spherical particles like liquid droplets , which is representative for the isometric domain (zone C). A value of SLDR^ is derived for all elevation angles from 90 and 150∘, leading to Fig. , which links our study to findings of showing distinct elevation-dependent signatures of SLDR for particles with different shapes. As illustrated in Fig. , prolate particles are characterized by nearly constant and relatively high values of SLDR at all elevation angles, which reach values of around -25 dB for solid columns and more than -20 dB for pronounced needles of high-axis ratio . The isometric primary particle shape class is represented by constantly low values of SLDR at all elevation angles between 90 and 150∘. Finally, plate-like particles, belonging to the oblate particle class, known to align predominantly horizontally along their planar planes, produce scattering similar to isometric particles observed at zenith-pointing (90∘ elevation angle) and will increasingly appear oblate at low elevation angles. That is why in the case of plate-like hydrometeors, SLDR, representative of the particle shape, is minimal at zenith-pointing and increases from 90 to 150∘ elevation angle. Indeed, at zenith-pointing, plate-like crystals have random orientation in the polarization plane, while at a low elevation angle horizontally aligned particles produce rather coherent returns in both polarimetric channels. Note that it is not directly possible to classify the type of isometric particles (e.g., aggregates or rimed particles can be isometric particles, too) since they have similar angular polarimetric signatures at all elevation angles. Discrimination between these types of particles can be made, e.g., using multiple-frequency observations but this is out of the scope of the current study. The VDPS method aims to differentiate the three main particle shape classes and their vertical evolution within cloud systems in order to determine microphysical processes occurring in mixed-phase clouds.

For each of the four individual scan patterns described in Fig. , the returned signals in the co- and cross-channel Pco(ωk) and Pcx(ωk), respectively, collected by MIRA-35 are saved in a level-0 file, in the pdm format defined by the company Metek. Consequently, the pdm data are in a first step converted into NetCDF format containing the polarimetric measurements of SLDR(ωk), calculated with Eq. (), as well as elevation angle and range. Next, the noise filtering (Eq. ()) is applied as explained in Sect.  and only the maximum spectral component of the remaining noise-free spectra is selected. Thus, arrays containing one value of SLDR per elevation angle are obtained for each granule of time and range. All range values are converted into height above ground, using the elevation angle θ as additional input. The VDPS algorithm runs automatically for each RHI scan selected. A main loop is used to separate the observations into multiple vertical “height” layers. In general, any arbitrary value of height resolution can be chosen. For the current study, each height step corresponds to the range resolution of MIRA-35 (31.18 m, i.e., the height resolution at zenith-pointing), as was done by . The following procedure is performed for each height layer which contains at least 20 values of SLDR from a full RHI scan recorded from 90∘ to 150∘ elevation angle (Fig. ). The value of 20 points per layer represents about 15% of the maximal number of data points. If this limit is not reached, it could mean that no cloud was detected at this layer or that not enough particles are contained at the investigated height level of the cloud, which would influence the quality of results. In this situation, the procedure will be stopped only for this layer at this step (no results are produced) and will continue to iterate into the next layer. If a sufficient number of data points was found at a height level, a new vector of SLDR(H,θ) is built. The elevation range of SLDR(H,θ) does not necessarily span the full elevation range of the RHI scan, as some data points at the elevation limits might have been removed.

As shown in Fig.  and as will be elaborated on further in Sect. , polarimetric signatures of different particle shapes are most visible when the elevation angle difference of the performed scans is large. For this reason, a full RHI scan is used to verify the homogeneity of the investigated cloud (Sect. ) and to calculate the SLDR linear regression (Sect. ), but only values of SLDR at two elevation angles are needed in the model output (Sect. ). In order to prepare the observational input for the evaluation against the spheroidal scattering model to be described in Sect. , we will look for the data points of SLDR associated with the smallest observed value of elevation angle (θmin, usually zenith-pointing) and to the largest value of elevation angle (θmax, usually 150∘). Thus, in a next step, fit values of measured SLDR at the minimum elevation angle θmin (SLDR(θmin)) and at maximum elevation angle θmax (SLDR(θmax)) are calculated. These notations will be used further in Sect. . It can be seen in Fig. , that the relationship between SLDR and the elevation angle is not linear for SLDR, especially in the case of oblate particles, and the more appropriate method to calculate SLDR(θmin) and SLDR(θmax) for all cases is to use a 3rd degree polynomial fit. SLDR(θmin) and SLDR(θmax) are determined with the fit values from the 3rd degrees polynomial fit at θmin and θmax, respectively. As an example, Fig.  shows the distribution of SLDR from θmin to θmax. Values of SLDR(θmin) and SLDR(θmax) are readable at 90∘ (θmin) and 150∘ (θmax) elevation angle as SLDR(θmin)=-32dB and SLDR(θmax)=-11dB. SLDR(θmin) and SLDR(θmax) are saved and will be utilized in Sect.  for the evaluation against the spheroidal scattering model compiled at the same elevation angles θmin and θmax.

In the first step of the VDPS retrieval we find two SLDR values corresponding to θmin and θmax (Sect. ). In the second step we search for values of the polarizability ratio and the degree of orientation for which the simulated SLDR^ fits to SLDR(θmin) and SLDR(θmax).

The original spheroidal scattering model based on does not take into account hardware-related effects and, therefore, predicts minimum values of SLDR^ that cannot be reached with the current radar technology due to the polarimetric coupling in the antenna system. The polarimetric coupling (co-cross-channel isolation) of the radar used is -35 dB, as mentioned in Sect. , and leads to an increased uncertainty of the retrieval for particles with polarizability ratio between 0.9 and 1.1. The modeled distribution of SLDR^ from 90 to 150∘ elevation angle for three exemplary particle habits oblate, isometric, and prolate is illustrated in Fig. . This graphic represents the theoretical relationship between SLDR^ and elevation angle in the three different primary particle shape classes, which is about to be faced with the direct measurements of SLDR. In the second part of this section, we compare the modeled SLDR^ and measured SLDR obtained from the polynomial fit (Sect. ) at elevation angles θmin and θmax, as explained in Sect. . In order to consider potential measurement inaccuracies, the 95% confidence interval Δ95 of the polynomial fit will be used to determine the potential range of the intersection. The confidence interval is calculated as follows: 3Δ95=2Δ, where Δ is the standard deviation of the difference between the measured and simulated values of SLDR at all available elevation angles from 90 to 150∘. The model is processed at θmin and θmax and the algorithm identifies isolines of SLDR(θmin)=SLDR^(θmin) ± Δ95, and SLDR(θmax)=SLDR^(θmax) ± Δ95, in the modeled fields of SLDR^ at θmin and θmax, respectively. For example, in Fig. a and b we can see the isoline where SLDR(θmin)=SLDR^(θmin) plotted in red and the isoline where SLDR(θmax)=SLDR^(θmax) plotted in blue on the model, respectively. The two isolines are plotted together in Fig. c, highlighting intersections between SLDR^(θmin), shown as a red curve, and SLDR^(θmax), shown as a blue curve, resulting in ξ=0.45 and ξ=2. If no intersection is found between SLDR^(θmin) and SLDR^(θmax), the algorithm searches for the point where the difference between SLDR^(θmin) and SLDR^(θmax) is the lowest. Finally, the algorithm characterizes the x-axis positions (polarizability ratio ξ) by deriving the mean and standard deviation of all overlapping data points included in each intersection between the isolines of SLDR^(θmin) and SLDR^(θmax) (Fig. ). Three values of ξ are saved at each height iteration corresponding to the three primary particle shape classes: the first intersection in the oblate particle shape class with ξ<1 (ξ=0.45 in Fig. c), the second intersection for the prolate particle shape class with ξ>1 (ξ=2 in Fig. c), and a mean of these two intersections for the isometric or low-density particle shape class with ξ≈1. The procedure could be repeated in a similar manner for determination of the possible y-axis values, which are the possible solutions of the degree of orientation κ, which is, however, not in the scope of our study.

The last step of the VDPS method consists of the identification of the primary particle shape class among the three possible solutions introduced in Sect.  and to quantify the primary particle shape class with the assigned value of ξ. As introduced in Sect. , the relationship between SLDR and the elevation angle is an important aspect to determine the particle shape and will be used in the following to discriminate between the primary particle shape classes. A threshold of ∂SLDR∂θ is determined in such a way that an unambiguous separation of the prolate, oblate, and isometric hydrometeor shape classes is possible, by applying a robust linear fit to all observed pairs of SLDR and elevation angle. The resulting limit values were derived to be limSLDR=0.1dB deg-1, as a threshold describing a certain change of the SLDR in dB per degree of elevation angle, and limpro=-25 dB, which describes the maximum value of SLDR to be associated to the prolate shape class. It should be noted that the two limit values might depend on the individual radar calibration. The actual shape class selection criteria are summarized in Table  and are described in the following. If the linear regression ∂SLDR∂θ exceeds limSLDR, particles are assigned to the oblate primary particle shape class. If ∂SLDR∂θ does not exceed limSLDR and if SLDR(θmin) and SLDR(θmax) exceed limpro, particles are assigned to the prolate primary particle shape class. If ∂SLDR∂θ does not exceed limSLDR and if SLDR(θmin) and SLDR(θmax) are below limpro, particles are associated to the isometric primary particle shape class. If particles are assigned to the isometric particle shape class, ξ will be calculated as the mean of the associated values of ξ contained in both intersections of SLDR^(θmin) and SLDR^(θmax) on both sides of ξ=1 (Sect. ). In the oblate and prolate primary particle shape classes, the error bars are calculated based on the intersections of the standard deviation obtained for SLDR^(θmin) and SLDR^(θmax), following the same procedure as explained in Sect. . Concerning the isometric primary particle shape class, ξ values of the two intersections identified before are used as error bars. Figure  depicts the relationship between SLDR and elevation angle from θmin to θmax. According to and , the relationship found is representative for oblate particles such as plate-like crystals, as depicted in Table . Regarding Fig. c presented in Sect. , we observe two intersections on both sides of ξ=1 and the choice of one of them requires an evaluation of the linear regression of SLDR from θmin to θmax. The associated distribution of SLDR presented in Fig.  confirms the assignment of ice particles to the oblate primary particle shape class due to the increase of SLDR from θmin to θmax and the exceeding of limSLDR. A value of ξ=0.45 is finally derived for this layer. The last step, according to the flow chart depicted in Fig. , is to apply the classification to the previously calculated profile of ξ (see Sect. ) and to store the selected values. This distribution of particle shape delivers information about the vertical profile of ice particle shapes in a cloud which is a relevant indicator for understanding in-cloud processes, illustrated in Sect. . The next section aims to evaluate and validate the VDPS method by means of three case studies, representing the three previously described particle shape classes prolate, oblate, and isometric, and to demonstrate the ability of the VDPS method to detect microphysical processes.

The first case study concentrates on the occurrence of rain, i.e., hydrometeors representative for the primary isometric particle shape class. Measurements were recorded on 13 February 2017 during an RHI scan from 13:31 to 13:33 UTC in Limassol. The studied cloud system, enframed by the black box in the Cloudnet target classification mask shown in Fig. , was identified to contain rain droplets at heights between 300 and 1300 m. The sudden drop of the melting layer height from 1300 m to around 1000 m height that is visible right at the time of the RHI scan is an artifact of the melting layer detection scheme of Cloudnet, which switched from a fall-velocity-based detection to the 0 ∘C-dewpoint level as threshold for the melting layer identification. However, the actual melting layer is well recognizable in Fig.  by means of the observed high values of SLDR at around 1300 m height. The Cloudnet classification indicates a mixed-phase layer at 1800 m height. For this case study, we are particularly interested in the rain from 300 to 1200 m height.

Figure  shows the RHI scan of SLDR from 90 to 150∘ elevation angle which was performed at 13:31 UTC. Values of SLDR from θmin to θmax are low (around -30 dB) and constant at heights below the melting layer, which is in agreement with what can be expected from scattering by isometric particles, as explained in Sect. . To illustrate this case study, we will focus only on one layer located at the height level from 868 to 899 m, represented by the black line on the y axis in Fig. . In Fig. b, the intersection of SLDR^(θmin) and SLDR^(θmax) is detectable by the red and blue curves which match the data of SLDR at θmin and θmax, respectively, with the simulated data SLDR^ from the spheroidal scattering model. We can distinctly notice the presence of two intersections between SLDR^(θmin) and SLDR^(θmax) from either side of the dashed red line, resulting in ξ=0.9 and ξ=1.1. In Fig. a, the slope of the linear regression ∂SLDR∂θ is constant between θmin and θmax where SLDR(θmin)<limpro and SLDR(θmax)<limpro and ∂SLDR∂θ<limSLDR. Regarding Table , this configuration describes the isometric primary particle shape class. Finally, the vertical distribution of ξ in the cloud is calculated following Sect.  and shown in Fig. . Concerning the observations, the melting layer is well identified by a variable ξ, as explained in the introduction of Sect. , in the height range from 1250 to 1350 m. Below this layer, ξ takes values around 1, which describes isometric or less dense particles (Sect. ). Looking at the Cloudnet classification (Fig. ), the drizzle-or-rain class dominates the measurement at heights below approximately 1000 m height, which can be extended to the melting layer at around 1300 m height, taking into account the misidentified drop due to the melting layer detection of Cloudnet, as previously explained. Figure  shows, in the black box, a temperature higher than 0 ∘C in this layer, which confirms the presence of liquid droplets, i.e., isometric particles. Application of the VDPS approach results in derivation of the same isometric primary particle shape class as determined based on the auxiliary observations (temperature and Cloudnet classification). With respect to the presented case it is noteworthy that it is likely that the observed rain droplets were small in size. This is corroborated by the absence of any elevation dependency of SLDR (Fig. ). In the case of strong rain, the oblateness of droplets would become apparent as SLDR increases from zenith pointing to 150∘ elevation angle, as we observed in some situations of convective rain in Limassol during the CyCARE campaign (Sect. ). Above the melting layer from 1700 to 2800 m height, the VDPS method derived isometric or less dense particles, as well. Given that temperatures are below freezing level at these heights and that Cloudnet identified a mix of ice and supercooled droplets, it is likely that these isometric or less dense particles are the result of mixed-phase cloud processes, such as riming or aggregation, which cannot unambiguously be identified solely with the VDPS method. Based on the VDPS method, the height level of the particle shape transition can be determined to be present at around 2800 m. Above, ξ was found to be well below 1, representing oblate particles, whose formation is also corroborated by the ambient temperatures of around -15 ∘C at this height level (see Fig. ). Applicability of the VDPS method is in the present case limited with respect to the interpretation of the microphysical process which led to the formation of the layer with isometric particle shape between approximately 1500 and 2700 m height. Doppler spectral methods or multi-frequency approaches could help here to investigate the possible contributions of riming and aggregation .

The second case study chosen to evaluate the VDPS method is dedicated to the characterization of columnar crystals. The corresponding measurement was recorded in Limassol on 8 December 2016 during an RHI scan from 00:31 to 00:33 UTC. Figure  presents the Cloudnet classification for the time range from 00:00 to 03:00 UTC on 8 December 2016, with the selected case study marked by the black frame. Figure  shows the RHI scans of SLDR from 90 to 150∘ elevation angle at 00:31 UTC.

In this RHI scan, high values of SLDR are observed at all elevation angles (between -20 and -15 dB), suggesting that the cloud is very homogeneous and that ice particles have a high capability to depolarize the returned radar signals. According to , particles having a SLDR from -20 to -15 dB can be classified at first glance as needles or hollow columns. This constellation excludes isometric particles and oblate particles and is a specific property of columnar crystals (see Table ). As for the first case study, the retrieval is visualized only for one specific layer, which in this case spans from 2458 to 2490 m height, indicated by the black line on the y axis in Fig. . Figure a shows the SLDR linear regression represented by the green line, which confirms that ∂SLDR∂θ<limSLDR. The polynomial fit represented by the red curve is used at θmin to θmax to calculate SLDR(θmin) and SLDR(θmax), as elaborated in Section . In Fig. b, once again two intersections of SLDR^(θmin) and SLDR^(θmax) exist for this layer. Considering the constant distribution (∂SLDR∂θ<limSLDR) and high values of SLDR (SLDR(θmin)>limpro and SLDR(θmax)>limpro), we can identify the intersection in the columnar particle shape class (see Table ), resulting in ξ>1 and κ<-0.8 as the most likely one. Figure  shows the vertical profile of ξ, which confirms the dominance of prolate particles in the investigated cloud. Accordingly, the Cloudnet classification, shown in Fig.  (black box), classifies the hydrometeors before the RHI scan as supercooled liquid droplets, and after the RHI scan as ice-containing and partly mixed-phase layer down to about 1500 m height. A rain event occurs a few minutes after the RHI scan, defining drizzle or rain. The temperature of the investigated case ranges from -3 ∘C at the cloud base and -7 ∘C at the cloud top. This temperature range is characteristic for the formation of hydrometeors in the columnar particle shape class, which demonstrates the ability of VDPS to derive prolate particles.

The third case study aims to describe oblate particles, such as plate-like crystals. The corresponding measurement was recorded in Limassol on 4 January 2017 during an RHI scan from 01:31 to 01:33 UTC. The observed cloud system is marked by the black frame in Fig. . The observation was characterized by the presence of a relatively homogeneous liquid-topped ice cloud in the height range from 3200 to 4200 m. Figure  shows the RHI scan of SLDR from 90 to 150∘ elevation angle at 01:31 UTC. An increase of SLDR from -30 to -10 dB between θmin and θmax is visible. The linear regression is represented by the green line in Fig. a, which exemplarily shows the retrieval for the layer from 3300 to 3331 m height, represented by the black line on the y axis in Fig. . In this case, ∂SLDR∂θ > limSLDR. SLDR(θmin) and SLDR(θmax) are calculated based on the values retrieved from the polynomial fit at θmin and θmax, i.e., the red curve represented in Fig. a. In Fig. b, we see two intersections between the isolines of SLDR^(θmin) and SLDR^(θmax). This configuration, associated with a positive linear regression of the polarimetric parameter SLDR (see Table ), implies selecting the intersection at ξ<1 and κ>0.8 for determination of the exact polarizability ratio, which corresponds to the oblate primary particle shape class. The vertical distribution of ξ presented in Fig.  indicates ξ<1 for all layers in the investigated cloud. The values of ξ are relatively constant around 0.4 from 3100 to 3600 m height corresponding to particles which are strongly oblate and rather dense, most likely pointing to the class of thick plate crystals . On the other hand, above 3600 m height, ξ≈0.55 was observed, representing particles which are likely less dense such as plates or dendritic crystals. In the Cloudnet classification shown in Fig. , where the period of approximately 1 h around the investigated RHI scan is indicated by the black rectangle, ice crystals and contributions of supercooled liquid droplets at the cloud top were identified. The temperature in the cloud ranges from -15 ∘C at the cloud top to -10 ∘C at the cloud base. Laboratory studies suggest that, in this temperature range, the primary formation of plate-like ice crystals is most likely to occur . Hence, there is a remarkably good agreement between results of the VDPS method and observations for this case study as well.

By means of a final case study, the potential of the VDPS method for exploration of the vertical evolution of particle shapes from the cloud top to the cloud base is discussed. The corresponding measurement was recorded in Limassol on 2 January 2017. In Fig. , the Cloudnet target classification mask of the observed cloud system is shown. The black frame in Fig.  highlights the time period around the RHI scan at 13:31 (vertical white bar), which will be analyzed here. As can be seen from the Cloudnet classification, ice crystals were identified at all heights from the cloud top (around 8500 m) down to the melting layer, which was classified at a height of around 1700 m. Only at heights between around 2000 and 2500 m were few data points of mixed-phase conditions identified. Also in Fig. , which shows the 13:31 UTC RHI scan of SLDR from 90 to 150∘ elevation angle, the melting layer is well represented at around 1700 m height by increased values of SLDR at all elevation angles. Focusing on the height range above the melting layer, the elevation dependency of SLDR shows a distinct evolution from the cloud top to the bottom. At the top of the cloud, at around 8000 m height, we can observe a strong increase of SLDR from θmin to θmax (-30 dB at θmin and -5 dB at θmax). Moving away from the cloud top toward the melting layer, the increase in SLDR from θmin to θmax becomes gradually less pronounced. Slightly above the melting layer (≈2000 m height), SLDR assumes values of around -30 dB at all elevation angles. The gradual change of the elevation dependency of SLDR from the cloud top to the cloud base translates into the vertical distribution of the polarizability ratio, as is illustrated in Fig. . From 8000 to 2000 m height, the polarizability ratio ξ increases gradually from 0.3, corresponding to very oblate and dense particles, such as plates, to 0.8 corresponding to less dense oblate particles, such as dendrites or aggregates. Between 2000 m height and the melting layer, located at 1700 m height, the polarizability ratio ξ is close to 1 corresponding to particles with low density or generally spherical particles. This gradual increase in ξ informs of a vertical change in particle shape while the ice crystals sedimented through the cloud system. As outlined earlier, a direct determination of the types of microphysical processes that occurred in this case cannot be achieved, as further constraints must be incorporated for a thorough interpretation as is outlined in Sect. .